NCTM Regionals -What’s the Point?

NCTM Regionals in Phoenix, AZ and Philadelphia, PA are going on this week and next (Phoenix, AZ is October 26-28, Philadelphia, PA is October 31 – November 2). The regional conferences are significantly smaller than the National conferences, and draw much more of a local group of math teachers versus the more wide-spread attendance, both national and international, at the NCTM Annual Conference (this year in San Antonio, TX, April 5-8, 2017). There use to be 3 regional conferences, and this year we are down to two, so the question arises, what’s the point? Are these Regional Conferences worth the time and effort? Well – as a math teacher who faithfully attended regional conferences for years and years, my answer is yes.

Here’s my short list of why there is in fact, a very definite “point’ to the NCTM Regionals:

  1. They are in the fall, after teachers have had a chance to get their classes going, image20understand their students, and get in the swing of things. It’s about the time when the dust has settled and teachers are looking for some new ideas, engaging activities, technology apps and devices – anything to help support student learning. The Regionals’ provide a chance to spark some creativity for teachers who are finally having some breathing room after the chaos of the start of a new school year.
  2. These are much more local conferences, so there’s a lot of teachers from the same area as both presenters and attendees – it builds some camaraderie, with many local schools and districts providing a day or two of professional learning time for their teachers to attend. It supports local math initiatives and provides teachers with new ideas and strategies that they then take back and share with other teachers and their students.
  3. The Regional conferences are less expensive, allowing for more teachers who want to attend to actually do so. Often times schools/districts will pay for teachers to go to the Regionals since they are a more affordable and they can send more teachers as well (more bang for their buck).
  4. keycurriculum_nctm2012-0442They occur early in a school year, so that math leaders and those who make ‘funding’ decisions can check out new curriculum, textbooks, technology, professional development, and math resources at the Exhibit Hall and at sessions. This allows for them to arrange for samples or pilots or meetings to plan for things like textbook adoptions or technology purchases or professional development support. Teachers often go to these Regional events and bring ideas back to their school leaders of what might be good for their schools/students. There is time to research, try-out, and get a feel for what resources might be best before any funding/purchases need to be made (usually the Spring).
  5. It provides a place to learn more about mathematics standards, Education Policy (like ESSA), standardized testing, and other math-related issues that impact teaching and student achievement
  6. It’s an opportunity for math educators to get together to collaborate, learn, share and get informed and rejuvenated about mathematics education. That’s the most important thing – educators learning together to find new and different ways to engage their students in mathematics learning. Nothing more powerful than that.

So – yes. There is a point. Hopefully there are many of you out there who are able toimage12 take
advantage of the NCTM Regionals this year. If not, the same can be said of your local and state math conferences, so don’t pass up the chance to attend those if you can.

Casio is in attendance at both Phoenix and Philadelphia NCTM Regionals, so be sure to stop by the booth and gets some hands-on play time with our technology and math resources. Not to mention entering the raffle for a free graphing calculator. We also have workshops happening at both conferences, so be sure to check those out as well.

Phoenix:

  1. Thursday, October 27
    • Exploring the Connection Between Recursive Sequences and Composition of Functions  Room 102 C, Grades 10-12, 9:30 – 10:30 am
    • You’ve Got To Move it! Transforming Mathematics – Room 227 AB, Grade Levels 8-10, 1:30 Pm – 2:45 pmimg_4198
  2. Friday October 28
    • Linear or Not Linear: That is the Question  Room 101AB, 8 – 9 am
    • The Probabilities of “Wheel of Fortune” – Room West 301A, 8 – 9 am

Philadelpha

  1. Tuesday, November 1
    • Problem Solving for Middle Grades Pre-Service Teachers   Room 105AB, Coaches/Leaders/Teacher Educators, 11:30 am – 12:30 pm
    • Polar, Parametric, Rectangular – Can You See the Connection?  Room Franklin 3/4, Grade Levels 10-12, 3:15-4:15 pm
  2. Wednesday, November 2
    • Hands-on Activities & Technology=Mathematical Understanding Through Authentic Modeling    Room Franklin 3/4, Grade 8-10, 9:45 – 11:00am
    • Exploring the Connection Between Recursive Sequences and Composition of Functions   Room 201B, Grades 8-10, 12:30 – 1:30 pm

 

Advertisements

Conics – Casio Prizm vs. TI-84+CE

I am currently teaching a course at Drexel University and we are starting a unit on circles. I loved using Sketchpad when teaching because it allowed for dynamic manipulation of objects (shapes, functions) so that students could visually see the impact of variables to the shape, size, position of the object. Unfortunately, my students (math teachers in a Masters Math Teaching Program) do not have access to Sketchpad, though one does use Geogebra, and as this is a course focused on teaching, they need to use what they have access to in their own classrooms with their students. For many of them this does not involve any technology at all, which is sad, but for some, they do have access to graphing calculators.

Naturally, this got me exploring what the graphing calculators could do, and surprise, surprise, I noticed quite a difference between the Casio Prizm and the TI-84+CE graphing calculators, which are the ones my class seems to have. I was investigating conics, and in particular circles, and what options the graphing calculators gave me, especially when thinking about dynamically modifying the variables to see how each impacts the graph of the circle. Here’s is a quick summary of what I found:

  1. Both TI-84 & Casio Prizm can graph conics (circles, ellipses, hyperbola, and parabola, though how to access these conic graphs is different on both.
    • It is more apparent/easy to find on the Casio (there is a Conic Graph menu).
    • TI requires knowing that there is a Conic app in the app menu, which is a button on the calculator. It is not seen from the main screen, and if you don’t know it exists, you won’t know it’s available.
  2. Both provide more than one equation form for each conic.
  3. Both show the graph of the conic, but how is very different.
    • Casio shows the graph on the coordinate grid, where you can see the whole grid, see values on each axis, and identify quadrant and key points on the graph
    • TI shows the graph in the entire window with a weird yellow frame around it. It is difficult to determine where on the coordinate grid the graph appears – there are axis marks, but no values, not origin, making it difficult for students to understand where on the coordinate grid the graph is. Very difficult to identify quadrant and key points on the graph.
  4. Both allow you to enter different values for each coefficient variable,
    • Casio has a modify feature that allows you to see the equation, graph, and coefficient variables on one screen. You can then modify one coefficient at a time and see it dynamically change on the graph, allowing students to visually see how each impacts the graph and see the conic change shape, location, and/or size.
    • TI84+CE only shows the graph or the equation/coefficients – never together.  You have to go back and forth between them when changing values. The TI does not clearly show where on the grid the graph is, does not show a size change (all conics look the same size, but the grid scale is changing). It’s actually very confusing and would be difficult to help student visually see the impact of changing coefficient variables on the size, location and shape.

Below is a video I made showing how to graph a circle and modify the coefficients on both calculators so you can see the differences I am talking about.

Hopefully you will come to the same conclusion I did – Casio Prizm is far superior when graphing conics than the TI84+CE.

Power bills as sources of math questions.

I’ve been thinking a lot about graphs lately, and how in general, many people are deceived by graphs because they don’t understand numbers, scale, sampling size, etc.  In this very contentious political time, it seems many people are fooled by the statistics they “see” graphically.  In my last post, I quoted Dan Finkel’s line “when we are not comfortable with math, we don’t question the authority of numbers”, specifically referencing people’s willingness to believe statistics they see or hear because they don’t really understand where these numbers came from or what they represent.

We can help our students get a better sense of statistics and numbers by providing them as many opportunities to explore, in context, graphs and statistics and ask questions and make sense of these. That could mean exploring all the statistics and poll results currently happening with the presidential election.  Or looking at weather predictions. As I looked at my power bill yesterday, I realized how easy this type of access to real numbers can be, as I stared at the graphical representation of my gas and electric over the past 13 months. (There is also a numerical table showing daily use of kilowat hours (kWh) and 100 (C) cubic feet volume of gas (Ccf). There alone is a whole bunch of mathematical calculation/conversions/ratios).  What I love about my graphical representations is there is a 13 month trend – so I can see where my usage was last year at the same month, and then see how my usage has changed throughout the year.  Below are my December & January graphical representations for both gas and electric usage.

ELECTRIC:

December Electric

December Electric

January electric

January Electric

 

GAS:

December Gas

December Gas

January Gas

January Gas

 

Just from these graphs, there are a lot of assumptions that can be made, and questions that could be asked, that would then lead to more exploration.  For example, December electric from 2014 and 2015 is about the same, but January 2015 is significantly less than January 2016 – why is that? (hint: my children are home for break, so we use more electricity). Gas use in December of 2015 was much lower – was this because it was warmer in December? Are we having a warmer winter than last year? The gas bills seem to show that – but, we could then go look at the weather temperatures for the same time frames in the area I live and see if there is a correlation between temperature and gas usage (i.e. heat). Why is the electric so much more in the spring/summer months and gas is lower? There are so many questions, and, if we brought in the tables of daily usage, cost of kWh and Ccf (volume) we could be doing math calculations, comparing costs, etc. Maybe compare bills from last year to this year and see if the price in oil/gas has had an impact on the overall monthly charge. I like the idea of bringing in the weather and comparing to the electric/gas usage. You can get average weather for the area you live in pretty easily, but it would be even better for students to collect actual temperatures over time and make their own graphs and comparisons.

2016-02-26_12-00-35

Average Climate Chart

The point I am making here is that a simple thing like a power bill can be a powerful tool for visualizing math, doing math, making connections, and asking questions. Or try looking at some statistics from car sales or stocks or polls on the presidential election. It leads kids to ask interesting questions, explore mathematics they care about, and opens them to the real-world aspect of mathematics and how numbers can be used to inform, deceive, and help make decisions.  These types of explorations are interesting and help students become involved in the world around them as well and better prepared for the realities of things like gas bills! Anyway, just another suggestion on how to bring some context into your math instruction in a relatively easy way.

 

 

 

 

 

 

 

 

 

 

Modifying Graphs with the Prizm – Check it out @NCTM Minneapolis

In preparation for NCTM Regionals in Minneapolis this week, I wanted to do a little show-and-tell with the Prizm. Hoping this sparks some interest and inspires some of you heading to the conference to stop by our booth (#511) at the conference and play with the Prizm.

One of the features of the Prizm that I just love is the ability to dynamically modify graphs, allowing students to visually see the effect of a coefficient on the graph of the function. This ability to modify one coefficient at a time and immediately see the impact on the graph allows students to make conjectures and get a better understanding of the graph and what each coefficient represents.

Here is a little demonstration of how the modify function works on the Prizm using both the standard form and vertex form of a quadratic:

I certainly hope you will stop by the booth Thursday or Friday and come play with us and learn more. I’d certainly love to meet you! Or, drop in on some sessions that utilize some of our products, like the Prizm, Keyboard and fx-55 Plus.

Thursday, November 12

  • Session 41 9:45 – 11:00, (M100 DE) Hand-held Technology + Hands-On Activities=CCSS Success -Tom Beatini
  • Session 84, 12:30-1:30, (M100 AB) CCSS for Statistics: Paired Quantitative Variables – John Diehl
  • Session 101, 1:30-2:45, (200 AB) Thinking Like A Synthesizer – Mike Reiners
  • Session 102, 2 – 3:00, (200 C) Connecting the Math through Meaningful Experiences – Jennifer North Morris